- CIRCULAR MOTION
- KINEMATICS OF CIRCULAR MOTION
- Important points
- Angular Velocity
- Important points
- Angular Acceleration
- Motion with constant angular velocity
- RELATION BETWEEN SPEED AND ANGULAR VELOCITY
- RELATIVE ANGULAR VELOCITY
- RADIAL AND TANGENTIAL ACCELERATION
- IMPORTANT POINT
- Calculation of centripetal acceleration
- DYNAMICS OF CIRCULAR MOTION
- RADIUS OF CURVATURE
- MOTION IN A VERTICAL CIRCLE
- CONDITION FOR OSCILLATION OR LEAVING THE CIRCLE
- CONDITION FOR LOOPING THE LOOP IN SOME OTHER CASES
- CIRCULAR TURNING ON ROADS
- By Friction Only
- By Banking of Roads Only
- By Friction and Banking of Road Both
- Note
- CENTRIFUGAL FORCE
- EFFECT OF EARTHS ROTATION ON APPARENT WEIGHT

When a particle moves in a plane such that its distance from a fixed (or moving) point

remains constant, then its motion is known as circular motion with respect to that fixed

(or moving) point

Read moreTo decide the angular position of a point in space we need to specify (i) origin and (ii) reference line.

The angle made by the position vector w.r.t. origin, with the reference line is called angular position.

Clearly angular position depends on the choice of the origin as well as the reference line.

Read moreInfinitesimally small angular displacement is a vector quantity, but finite angular displacement is a

scalar, because while the addition of the Infinitesimally small angular displacements is commutative,

addition of finite angular displacement is not.

Read moreInstantaneous Angular Velocity

It is the limit of average angular velocity as ?t approaches zero. i.e.

Read moreAngular velocity has dimension of [T-1] and SI unit rad/s.

Read moreInstantaneous Angular Acceleration :

It is the limit of average angular acceleration as ?t approaches zero, i.e.,

Read more? ? Angular displacement

Circular motion with constant angular acceleration is analogous to one dimensional translational motion with

constant acceleration. Hence even here equation of motion have same form.

Read moreRELATION BETWEEN SPEED AND ANGULAR VELOCITY

Read moreJust as velocities are always relative, similarly angular velocity is also always relative. There is no such thing as

absolute angular velocity. Angular velocity is defined with respect to origin, the point from which the position

vector of the moving particle is drawn.

Read moreThere are two types of acceleration in circular motion ; Tangential acceleration and centripetal acceleration

Read moreDifferentiation of speed gives tangential acceleration

Read moreConsider a particle which moves in a circle with constant speed v as shown in figure

Read moreIf there is no force acting on a body it will move in a straight line (with constant speed). Hence if a body is moving

in a circular path or any curved path, there must be some force acting on the body.

If speed of body is constant, the net force acting on the body is along the inside normal to the path of the body

and it is called centripetal force.

Read moreAny curved path can be assumed to be made of infinite circular arcs. Radius of curvature at a point is the radius

of the circular arc at a particular point which fits the curve at that point.

Read moreLet us consider the motion of a point mass tied to a string of

length and whirled in a vertical circle. If at any time the body

is at angular position ?, as shown in the figure, the forces

acting on it are tension T in the string along the radius towards

the center and the weight of the body mg acting vertically

down wards.

Read morevertical plane. In this case, the motion of the point mass which depend on

‘whether tension becomes zero before speed becomes zero or vice versa

Read moreCONDITION FOR LOOPING THE LOOP IN SOME OTHER CASES

Case 1 : A mass moving on a smooth vertical circular track.

Read moreWhen vehicles go through turnings, they travel along a nearly circular

arc. There must be some force which will produce the required centripetal

acceleration. If the vehicles travel in a horizontal circular path,

this resultant force is also horizontal. The necessary centripetal force

is being provided to the vehicles by following three ways.

Read moreSuppose a car of mass m is moving at a speed v in a horizontal circular arc of radius r. In this case,

the necessary centripetal force to the car will be provided by force of friction f acting towards center

Read moreFriction is not always reliable at circular turns if high speeds and sharp turns are involved to avoid dependence on

friction, the roads are banked at the turn so that the outer part of the road is some what lifted compared to the

inner part.

Read moreIf a vehicle is moving on a circular road which is rough and banked also, then three forces may act on the vehicle,

of these the first force, i.e., weight (mg) is fixed both in magnitude and direction.

Read moreThe expression tan ? = rg

v2

also gives the angle of banking for an aircraft, i.e., the angle through

which it should tilt while negotiating a curve, to avoid deviation from the circular path.

Read moreWhen a body is rotating in a circular path and the centripetal force vanishes, the body would leave the circular

path. To an observer A who is not sharing the motion along the circular path, the body appears to fly off tangentially

at the point of release. To another observer B, who is sharing the motion along the circular path (i.e., the

observer B is also rotating with the body which is released, it appears to B, as if it has been thrown off along the

radius away from the centre by some force. This inertial force is called centrifugal force.)

Read moreThe earth rotates about its axis at an angular speed of one revolution per 24

hours. The line joining the north and the south poles is the axis of rotation.

Every point on the earth moves in a circle. A point at equator moves in a circle of

radius equal to the radius of the earth and the centre of the circle is same as the

centre of the earth. For any other point on the earth, the circle of rotation is

smaller than this. Consider a place P on the earth (figure).

Read more